Remarks on automatic algorithm stabilization

Kiyoshi Shirayanagi
NTT Communication Science Laboratories
- Moss Sweedler¹
Department of Mathematics, Cornell University

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Abstract:

Approximate algebra typically deals with inexact input, perhaps due to constraints of physical measurement, and aims to arrive at appropriate approximate output. This article deals with inexact computation for another purpose. It is about a methodology utilizing inexact computation in conjunction with exact computation where the exact input is known and exact output is desired. The inexact computation is used to help avert the growth of intermediate expressions which frequently make simply using exact computation infeasible. The paper describes the methodology and how to make good use of it. The paper surveys several existing applications and proposes new areas or directions for future applications. It also briefly addresses frequently asked questions and misunderstandings.